The 2016-2018 capital budget had not only increased the cost of the project from $4 million to $5.5 million, but also pushed funding for the construction back two years.

Legislator Jay Schneiderman confirmed on Tuesday afternoon that he secured the votes necessary in the capital budget’s “working group” — a committee of nine legislators — to get $4 million in funding for the project next year. He said Legislators Kara Hahn, Kate Browning, Monica Martinez and Presiding Officer DuWayne Gregory all voted in favor of restoring the funding — though he wasn’t sure he had the votes until roll call actually came.

“I was sweating bullets,” he said. In the end, he said, Ms. Browning’s vote came as unexpected. Mr. Schneiderman credited Southampton Councilwoman Bridget Fleming — who is running to fill Mr. Schneiderman’s seat in the fall — for going to the meeting to attest to its importance.

“I have to credit Bridget,” he said. “Having her there really helped.”

Now, the full legislature will have to approve all of the working group’s suggestions at its June 2 meeting.

The reconfiguration will make the traffic circle oval-shaped and two lanes. Supporters of the project said last week that it could hold up private investment in the community — considered one of Suffolk County’s most economically-distressed areas — at a time when other efforts are being made to improve the area.

Renaissance Downtowns was hired by Southampton Town last year as a “master developer” to craft zoning plans for the area. The for-profit company — which can purchase land from property owners in the area or help them develop the land themselves — presented their plans last month.

Siris Barrios, a community liaison with Riverside Rediscovered — the name of Renaissance Downtown’s revitalization effort in Riverside — said on Tuesday that “this is a victory on so many levels.” Riverside Rediscovered started an online petition in an effort to keep the $4 million budgeted for 2016.

“Yes, we got the funding back in 2016,” she said. “But this will help send a message to investors that Suffolk County is serious about revitalization … and honestly, one of the key things for me is the empowerment of this community. They got politically engaged — face-to-face and online — which is a community victory. They helped secure $4 million back. That’s major.”

Riverside Rediscovered will be holding a party at its Peconic Avenue office next Tuesday at 6:30 — possibly after the full legislature votes to make it official — to celebrate the victory.